Finite quotients of braid groups have large sizes.
problem Understanding the size of finite quotients of braid groups.
method Derived lower bounds on the size of quotients.
result Lower bounds are superexponential in the number of strands.
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48 results for “quotient size”
New theorem bounds group quotient size to subgroups index.
problem Understanding subgroup structure in hyperbolic groups.
method Proved quotient size bounds on Eilenberg-MacLane spaces.
result One-ended hyperbolic groups cannot have isomorphic finite-index subgroups.
Sharp bounds found on nonabelian quotients of surface braid groups.
problem Finding the smallest nonabelian quotients of surface braid groups.
method Sharp lower bounds and classification of quotients.
result Quotients of minimum order are either symmetric groups or 2-step nilpotent p-groups.
We show that for any positive integer , -relator quotients of the modular group generically satisfy a very strong Mostow-type \emph{isomorphism rigidity}. We also prove that such quotients are generically "essentially incompressible". By this we mean that their "absolute -invariant…
The paper studies finiteness of canonical quotients in Dehn quandles of surfaces.
problem Finiteness of canonical quotients in Dehn quandles of surfaces.
method Analyzing the Dehn quandle structure and using quandle quotients.
result For surfaces of positive genus, the -quandle of their Dehn quandles is finite for specific values of .
We present a novel tractable generative model that extends Sum-Product Networks (SPNs) and significantly boosts their power. We call it Sum-Product-Quotient Networks (SPQNs), whose core concept is to incorporate conditional distributions into the model by direct computation using quotient nodes, e.g. $P(A|B) = \frac{P(…
We study non-linear sigma models whose target spaces are the Higgs phases of supersymmetric SO and USp gauge theories by using the Kahler and hyper-Kahler quotient constructions. We obtain the explicit Kahler potentials and develop an expansion formula to make use of the obtained potentials from which we also calculate…
In this article, we study connections between representation theory and efficient solutions to the conjugacy problem on finitely generated groups. The main focus is on the conjugacy problem in conjugacy separable groups, where we measure efficiency in terms of the size of the quotients required to distinguish a distinc…
In this work the Isoperimetric Inequality for integral varifolds is used to obtain sharp estimates for the size of the set where the density quotient is small and to generalise Calderón's and Zygmund's theory of first order differentiability for functions in Lebesgue spaces from Lebesgue measure to integral varifolds.
Study improves neural network generalization for invariant and equivariant data.
problem Developing a generalization theory for invariant and equivariant neural networks.
method Introducing quotient feature spaces to measure the effect of group actions on properties and proving a generalization error bound.
result The volume of quotient feature spaces can describe the generalization error and invariance/equivariance significantly improve the bound.
We construct pairs of compact Riemannian orbifolds which are isospectral for the Laplace operator on functions such that the maximal isotropy order of singular points in one of the orbifolds is higher than in the other. In one type of examples, isospectrality arises from a version of the famous Sunada theorem which als…
The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski to…
New computations show symplectic groups and mapping class groups have different properties regarding torsion.
problem Comparing properties of symplectic groups and mapping class groups.
method Using -theory, Weil representations, and quantum representations.
result Symplectic groups have uniformly bounded torsion, while mapping class groups have more complex torsion.
We study the limits of sequences of spheres and complex projective spaces with unbounded dimensions. A sequence of spheres (resp. complex projective spaces) either is a Levy family, infinitely dissipates, or converges to (resp. the Hopf quotient of) a virtual infinite-dimensional Gaussian space, depending on the size o…
The paper studies hyperbolic quotients of projection complexes and their actions.
problem Understanding the structure and properties of quotients of projection complexes.
method Analyzing the quotient of projection complexes by normal subgroups and studying the resulting actions.
result The quotient complex is δ-hyperbolic under certain conditions, and the quotient group is acylindrically hyperbolic.
Study quotients of curve complex actions by mapping class group.
problem Understanding actions of mapping class group on curve complex quotients.
method Cone off uniformly quasi-convex subspaces to form symmetric curve sets, non-maximal train track sets, and compression body disc sets. Analyze actions of mapping class group on these quotients.
result Actions of mapping class group on quotients are strongly WPD, non-elementary, and have infinite diameter.
Study finds smallest non-trivial quotients of braid groups and commutator subgroups.
problem Identifying smallest non-trivial quotients of braid groups and commutator subgroups.
method Analyzing symmetric and alternating groups for quotients of braid groups and commutator subgroups.
result Proved smallest quotients for specific braid groups and commutator subgroups.
In this paper, we propose a weak version of quotient for the algebraic action of a group on a variety, which we shall call a pseudo-quotient. They arise when we focus on the purely topological properties of good GIT quotients regardless of their algebraic properties. The flexibility granted by their topological nature …
In this paper, we investigate the existence of a subclass of quotients of affine connection control systems, which preserve the mechanical structures. Both local and global sufficient and necessary conditions are given for the geodesically accessible affine connection control systems such that they can admit this subcl…
Paper compares total quotient curvature and proves bounds for Einstein metric.
problem Comparing total quotient curvature and proving bounds for Einstein metric.
method Established comparison theorems and proved integral inequalities.
result Background Einstein metric achieves a sharp bound on total quotient curvature.
Establishes a concavity property for positive Hessian quotient operators.
problem Analyzing positive Hessian quotient operators on Riemannian manifolds.
method Proves a special concavity property and a Jacobi inequality.
result Proves a Jacobi inequality for symmetric tensors.
Paper examines properties of specific solutions to Yamabe flow.
problem Characterizing quotient almost Yamabe solitons.
method Investigates quotient almost Yamabe solitons and presents conditions for their rigidity.
result Sufficient conditions for quotient almost Yamabe solitons to be trivial or isometric with a sphere.
We study Deraux's non arithmetic orbifold ball quotient surfaces obtained as birational transformations of a quotient of a particular Abelian surface . Using the fact that is the Jacobian of the Bolza genus curve, we identify as the weighted projective plane . We compute the equati…
Generalised spin structures, or r-spin structures, on a 2-dimensional orbifold Σare r-fold fibrewise connected coverings (also called r-th roots) of its unit tangent bundle STΣ. We investigate such structures on hyperbolic orbifolds. The conditions on r for such structures to exist are given. The action of the diffeomo…
Study shows quotient group is infinitely generated.
problem Understanding the structure of homology cobordism groups.
method Proved using Seifert fibered spaces.
result Quotient group is infinitely generated.
We solved a conjecture about braid group quotients being alternating groups.
problem Understanding the smallest non-trivial quotients of braid group commutator subgroups.
method Proved the conjecture about alternating groups as quotients, showed minimal quotient maps.
result Proved conjecture about braid group quotients being alternating groups.
The study shows how quotients of mapping class groups are hierarchically hyperbolic.
problem Understanding the hierarchical hyperbolicity of mapping class groups and their quotients.
method A combinatorial criterion for hierarchical hyperbolicity applied to mapping class groups.
result Quotients of mapping class groups by large powers of Dehn twists are hierarchically hyperbolic.
Study on Kohn Laplacian spectrum on sphere quotients.
problem Determining fundamental group from Kohn Laplacian spectrum.
method Weyl-type theorem, CR manifolds, Sobolev estimates.
result Fundamental group can be determined from Kohn Laplacian spectrum in 3D.
Algorithm distinguishes Fuchsian groups with finite quotients.
problem Distinguishing between non-isomorphic Fuchsian groups.
method Develops an algorithm to create group extensions using finite quotients.
result Establishes an upperbound for the order of a distinguishing finite quotient.
Cusped spaces for hierarchically hyperbolic groups, and applications to Dehn filling quotientsmath.GT
Study of Dehn filling quotients in hierarchically hyperbolic groups.
problem Understanding the structure of Dehn filling quotients in specific groups.
method Introduced a construction for cusped spaces of relatively hyperbolic groups and used it to study Dehn-filling-like quotients.
result Infinite hyperbolic quotients of mapping class groups of punctured spheres and braid groups are found.
The paper studies Lie algebroid and groupoid quotients with forms, applying to Poisson and Dirac structures.
problem Understanding quotients of Lie algebroids and groupoids with compatible differential forms.
method Identifying Lie theoretic conditions for forms to be basic, characterizing induced forms on quotients, and applying results to Poisson and Dirac structures.
result Recovery and generalization of known results on Poisson reduction.
Reductive quotients preserve klt singularities in algebraic geometry.
problem Preserving klt singularities in quotients of klt singularities.
method Proving that the quotient of a klt type singularity by a reductive group is of klt type.
result The quotient of a klt variety by a reductive group results in a klt variety with a suitable boundary.
Center and torsion of a quotient of the group of piecewise linear homeomorphisms of the real linemath.GT
The center of a quotient group of piecewise linear homeomorphisms is trivial.
problem Understanding the structure of a specific group of homeomorphisms.
method Analyzing a quotient of piecewise linear homeomorphisms of the real line.
result The center of the quotient group is trivial.
The study provides interior curvature estimates for convex graphs satisfying a specific quotient equation.
problem Interior curvature estimates for convex graphs.
method Analyzes convex graphs satisfying the quotient equation .
result Interior curvature estimates for convex graphs.
Quotients of torus endomorphisms have parabolic orbifolds.
problem Understanding the structure of quotients of torus endomorphisms.
method Analyzing the properties of torus endomorphisms and their quotients.
result Every quotient of a torus endomorphism has a parabolic orbifold.
Short note finds a new metric from sphere quotients.
problem Finding metrics from sphere quotients.
method Conformal stereographic projection on sphere quotients.
result Result is a Majumdar-Papapetrou metric.
Study non-existence of complex ball quotients in Torelli locus.
problem Non-existence of totally geodesic complex ball quotients in Torelli locus.
method Analytic techniques.
result Analytic techniques used to study non-existence.
Paper studies Hessian quotient equations in warped product manifolds.
problem Analyzing Hessian quotient equations in warped product manifolds.
method Using standard degree theory and a priori estimates.
result Existence of star-shaped compact hypersurface solutions.
Study proves estimate for Hessian quotient equations on 2D Riemannian manifolds.
problem Problems posed by Delanoë and Urbas related to Hessian quotient equations.
method Maximum principle argument and new test function introduced to prove estimate.
result Unobstructed second order a priori estimate for real Hessian quotient equation in 2D.
Random quotients preserve hyperbolic properties in groups.
problem Preserving hyperbolic properties in random group quotients.
method Independent random walks, spinning families, projection complexes.
result Random quotients of acylindrical and hierarchical hyperbolic groups remain so.
Random quotients of mapping class groups have rigid properties.
problem Rigidity of random quotients of mapping class groups.
method Generalization of Ivanov's theorem and use of hierarchically hyperbolic groups.
result Automorphisms and commensurators of random quotients coincide with the groups themselves.
We study a quotient of the group algebra of the braid group in which the Artin generators satisfy a cubic relation. This quotient is maximal among the ones satisfying such a cubic relation. It is finite-dimensional for at least n at most 5 and we investigate its module structure in this range. We also investigate the p…
Estimates solutions to Hessian quotient equations on HKT manifolds.
problem Finding estimates for solutions to Hessian quotient equations.
method Using the cone condition directly to show estimates.
result Showed estimates for solutions to Hessian quotient equations on HKT manifolds.
Quotient manifolds of flowsmath.DS
This paper investigates which smooth manifolds arise as quotients (orbit spaces) of flows of vector fields. Such quotient maps were already known to be surjective on fundamental groups, but this paper shows that every epimorphism of countably presented groups is induced by the quotient map of some flow, and that higher…
Study on braid groups' congruence subgroups and their crystallographic quotients.
problem Understanding congruence subgroups and crystallographic quotients of braid groups.
method Investigation of lower central series of congruence braid groups related to .
result Quotients of congruence braid groups are almost crystallographic.
This paper classifies all admissible quotients of a surface braid group up to order 127.
problem Classifying admissible quotients of surface braid groups with bounded order.
method Analyzing finite quotients of the pure braid group on two strands of a Riemann surface.
result All admissible quotients of the braid group have order at most 127.
Proves a representation that separates a subgroup in RAAGs.
problem Separating a word quasiconvex subgroup in RAAGs.
method Finite dimensional representation of L that separates H in the induced Zariski topology.
result Establishes a polynomial upper bound on the size of the quotients used to separate H in L.
We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the -invariant of Tian, and utilize it to classify four-dimensional and five-dimensional exceptional quotient singularities.